The Republicans should get as much as they can in spending cuts and entitlement reform. Loudly disagree with tax increases (call them tax increases no matter what the left wants to call them).
Announce the deal that the democrats can pass the legislation in the Senate and that the house will arrange republican votes so that the democrats can pass the legislation only if they all vote for it.
through every avenue they can the republicans should announce that this isn't their idea of a good deal, but that We the People have given control to the Democrats. Then let 'em vote.
If the tax increases pass and the spending reform doesn't get done - it's a simple job of reminding people daily who voted them into economic chaos.